docs(agents): document Cursor Cloud dev environment setup for v5 (Bun)

[dylantientcheu]

What

Sets up and verifies the Cloud dev environment for the v5 branch (Bun-based) and records durable, non-obvious startup notes in AGENTS.md under ## Cursor Cloud specific instructions.

The only code change is documentation (AGENTS.md). The startup update script is configured to bun install.

Environment

• Node 22.15.0 via fnm, Bun 1.3.10 (pinned in .tool-versions).
• bun install links all workspaces.

Verification

Check	Command	Result
Type check	bun run test:types	✅ pass
Lint (ESLint)	bun run lint	✅ pass
Lint (CSS)	bun run lint:css	⚠️ runs; reports pre-existing repo violations
Unit tests	bun run test --run	✅ 214 passed (24 files)
Build (libs)	bun run --sequential build:stage:base build:stage:react build:stage:consumers build:stage:adapter	✅ pass
Build (full)	bun run build	❌ fails at website:build (see caveat)
Run/demo	bun run playground:start → http://localhost:5173	✅ live Algolia search working

Hello-world demo

Opened the React playground, opened the DocSearch modal, typed getting started, got live Algolia results, and navigated to a result.

docsearch_v5_playground_search_demo.mp4

Live search results for

Known caveat (documented in AGENTS.md)

The Docusaurus website does not run under Bun on this branch: both website:build and the dev server fail with ERR_PACKAGE_PATH_NOT_EXPORTED (entities/cheerio transitive deps under Bun's hoisting). This blocks full bun run build and Playwright E2E (pw:*), which boots the website first. Library builds and the playground demo are unaffected.

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